LMFDB - Embedded newform 600.2.bp.b.317.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(53,600)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 10, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("600.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bp (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	16.0.6879707136000000000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{12} + 81x^{8} - 729x^{4} + 6561 $ x^16 - 9x^12 + 81x^8 - 729*x^4 + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{20}]$

Embedding invariants

Embedding label			317.1
Root			$1.54327 + 0.786335i$ of defining polynomial
Character	$\chi$	$=$	600.317
Dual form			600.2.bp.b.53.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642040 - 1.26007i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(0.473739 + 2.18531i) q^{5} +(1.98168 + 1.43977i) q^{6} +(-3.20022 - 3.20022i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(3.05781 + 0.806108i) q^{10} +(-1.07155 - 3.29791i) q^{11} +(3.08654 - 1.57267i) q^{12} +(-6.08718 + 1.97785i) q^{14} +(-3.86682 + 0.218323i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-3.00000 + 3.00000i) q^{18} +(2.97899 - 3.33551i) q^{20} +(6.34181 - 4.60759i) q^{21} +(-4.84359 - 0.767149i) q^{22} -4.89898i q^{24} +(-4.55114 + 2.07053i) q^{25} +(2.35900 - 4.62981i) q^{27} +(-1.41598 + 8.94015i) q^{28} +(-5.49489 - 7.56307i) q^{29} +(-2.20755 + 5.01266i) q^{30} +(-7.96171 - 5.78452i) q^{31} +(4.00000 + 4.00000i) q^{32} +(5.93216 - 0.939561i) q^{33} +(5.47740 - 8.50954i) q^{35} +(1.85410 + 5.70634i) q^{36} +(-2.29036 - 5.89527i) q^{40} +(-1.73422 - 10.9494i) q^{42} +(-4.07644 + 5.61073i) q^{44} +(0.674235 - 6.67423i) q^{45} +(-6.17307 - 3.14534i) q^{48} +13.4828i q^{49} +(-0.312992 + 7.06414i) q^{50} +(-2.27150 + 14.3417i) q^{53} +(-4.31932 - 5.94504i) q^{54} +(6.69931 - 3.90402i) q^{55} +(10.3561 + 7.52417i) q^{56} +(-13.0580 + 2.06818i) q^{58} +(13.6913 + 4.44859i) q^{59} +(4.89898 + 6.00000i) q^{60} +(-12.4006 + 6.31845i) q^{62} +(6.16401 + 12.0975i) q^{63} +(7.60845 - 2.47214i) q^{64} +(2.62476 - 8.07819i) q^{66} +(-7.20594 - 12.3654i) q^{70} +(8.38081 + 1.32739i) q^{72} +(2.64744 + 1.34894i) q^{73} +(-2.30897 - 8.34678i) q^{75} +(-7.12482 + 13.9832i) q^{77} +(-8.25966 - 11.3684i) q^{79} +(-8.89898 - 0.898979i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-5.53525 + 0.876698i) q^{83} +(-14.9105 - 4.84471i) q^{84} +(14.4272 - 7.35102i) q^{87} +(4.45270 + 8.73892i) q^{88} +(-7.97714 - 5.13471i) q^{90} +(12.0530 - 12.0530i) q^{93} +(-7.92672 + 5.75910i) q^{96} +(-4.97879 - 0.788563i) q^{97} +(16.9894 + 8.65651i) q^{98} +10.4029i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{5} + 4 q^{7} - 8 q^{8} + 8 q^{10} - 24 q^{11} - 12 q^{15} + 16 q^{16} - 48 q^{18} - 8 q^{20} + 36 q^{21} - 16 q^{22} + 32 q^{28} + 12 q^{30} + 64 q^{32} + 12 q^{33} + 8 q^{35} - 24 q^{36}+ \cdots + 72 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 4 * q^5 + 4 * q^7 - 8 * q^8 + 8 * q^10 - 24 * q^11 - 12 * q^15 + 16 * q^16 - 48 * q^18 - 8 * q^20 + 36 * q^21 - 16 * q^22 + 32 * q^28 + 12 * q^30 + 64 * q^32 + 12 * q^33 + 8 * q^35 - 24 * q^36 + 24 * q^42 - 48 * q^45 - 4 * q^50 + 28 * q^55 - 24 * q^56 - 8 * q^58 + 80 * q^59 + 12 * q^63 + 36 * q^66 - 32 * q^70 + 24 * q^72 - 28 * q^73 - 24 * q^75 - 12 * q^77 - 64 * q^80 + 36 * q^81 + 24 * q^83 - 36 * q^87 + 32 * q^88 + 24 * q^93 - 16 * q^97 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{13}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.642040	−	1.26007i	0.453990	−	0.891007i
$2$	0.642040	−	1.26007i	0.453990	−	0.891007i
$3$	−0.270952	+	1.71073i	−0.156434	+	0.987688i
$3$	−0.270952	+	1.71073i	−0.156434	+	0.987688i
$4$	−1.17557	−	1.61803i	−0.587785	−	0.809017i
$5$	0.473739	+	2.18531i	0.211862	+	0.977299i
$5$	0.473739	+	2.18531i	0.211862	+	0.977299i
$6$	1.98168	+	1.43977i	0.809017	+	0.587785i
$7$	−3.20022	−	3.20022i	−1.20957	−	1.20957i	−0.971166	−	0.238404i	$-0.923376\pi$
$7$	−3.20022	−	3.20022i	−1.20957	−	1.20957i	−0.238404	−	0.971166i	$-0.576624\pi$
$8$	−2.79360	+	0.442463i	−0.987688	+	0.156434i
$9$	−2.85317	−	0.927051i	−0.951057	−	0.309017i
$10$	3.05781	+	0.806108i	0.966964	+	0.254914i
$11$	−1.07155	−	3.29791i	−0.323086	−	0.994356i	−0.972297	−	0.233748i	$-0.924901\pi$
$11$	−1.07155	−	3.29791i	−0.323086	−	0.994356i	0.649211	−	0.760608i	$-0.275099\pi$
$12$	3.08654	−	1.57267i	0.891007	−	0.453990i
$13$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$13$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$14$	−6.08718	+	1.97785i	−1.62687	+	0.528601i
$15$	−3.86682	+	0.218323i	−0.998410	+	0.0563708i
$16$	−1.23607	+	3.80423i	−0.309017	+	0.951057i
$17$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$17$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$18$	−3.00000	+	3.00000i	−0.707107	+	0.707107i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	2.97899	−	3.33551i	0.666122	−	0.745843i
$21$	6.34181	−	4.60759i	1.38390	−	1.00546i
$22$	−4.84359	−	0.767149i	−1.03266	−	0.163557i
$23$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$23$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$24$		−	4.89898i		−	1.00000i
$25$	−4.55114	+	2.07053i	−0.910229	+	0.414106i
$26$		0			0
$27$	2.35900	−	4.62981i	0.453990	−	0.891007i
$28$	−1.41598	+	8.94015i	−0.267595	+	1.68953i
$29$	−5.49489	−	7.56307i	−1.02038	−	1.40443i	−0.911940	−	0.410323i	$-0.865416\pi$
$29$	−5.49489	−	7.56307i	−1.02038	−	1.40443i	−0.108436	−	0.994103i	$-0.534584\pi$
$30$	−2.20755	+	5.01266i	−0.403042	+	0.915182i
$31$	−7.96171	−	5.78452i	−1.42996	−	1.03893i	−0.990023	−	0.140904i	$-0.954999\pi$
$31$	−7.96171	−	5.78452i	−1.42996	−	1.03893i	−0.439941	−	0.898027i	$-0.645001\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	5.93216	−	0.939561i	1.03266	−	0.163557i
$34$		0			0
$35$	5.47740	−	8.50954i	0.925850	−	1.43837i
$36$	1.85410	+	5.70634i	0.309017	+	0.951057i
$37$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$37$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$38$		0			0
$39$		0			0
$40$	−2.29036	−	5.89527i	−0.362137	−	0.932125i
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$	−1.73422	−	10.9494i	−0.267595	−	1.68953i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	−4.07644	+	5.61073i	−0.614546	+	0.845850i
$45$	0.674235	−	6.67423i	0.100509	−	0.994936i
$46$		0			0
$47$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$47$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$48$	−6.17307	−	3.14534i	−0.891007	−	0.453990i
$49$			13.4828i			1.92612i
$50$	−0.312992	+	7.06414i	−0.0442638	+	0.999020i
$51$		0			0
$52$		0			0
$53$	−2.27150	+	14.3417i	−0.312014	+	1.96998i	−0.0830438	+	0.996546i	$0.526464\pi$
$53$	−2.27150	+	14.3417i	−0.312014	+	1.96998i	−0.228970	+	0.973433i	$0.573536\pi$
$54$	−4.31932	−	5.94504i	−0.587785	−	0.809017i
$55$	6.69931	−	3.90402i	0.903334	−	0.526419i
$56$	10.3561	+	7.52417i	1.38390	+	1.00546i
$57$		0			0
$58$	−13.0580	+	2.06818i	−1.71459	+	0.271565i
$59$	13.6913	+	4.44859i	1.78246	+	0.579157i	0.999100	−	0.0424110i	$-0.0135039\pi$
$59$	13.6913	+	4.44859i	1.78246	+	0.579157i	0.783360	+	0.621568i	$0.213504\pi$
$60$	4.89898	+	6.00000i	0.632456	+	0.774597i
$61$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$61$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$62$	−12.4006	+	6.31845i	−1.57488	+	0.802443i
$63$	6.16401	+	12.0975i	0.776592	+	1.52415i
$64$	7.60845	−	2.47214i	0.951057	−	0.309017i
$65$		0			0
$66$	2.62476	−	8.07819i	0.323086	−	0.994356i
$67$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$67$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$68$		0			0
$69$		0			0
$70$	−7.20594	−	12.3654i	−0.861274	−	1.47795i
$71$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$71$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$72$	8.38081	+	1.32739i	0.987688	+	0.156434i
$73$	2.64744	+	1.34894i	0.309859	+	0.157881i	0.602004	−	0.798493i	$-0.294369\pi$
$73$	2.64744	+	1.34894i	0.309859	+	0.157881i	−0.292145	+	0.956374i	$0.594369\pi$
$74$		0			0
$75$	−2.30897	−	8.34678i	−0.266617	−	0.963803i
$76$		0			0
$77$	−7.12482	+	13.9832i	−0.811948	+	1.59354i
$78$		0			0
$79$	−8.25966	−	11.3684i	−0.929284	−	1.27905i	−0.960138	−	0.279526i	$-0.909823\pi$
$79$	−8.25966	−	11.3684i	−0.929284	−	1.27905i	0.0308541	−	0.999524i	$-0.490177\pi$
$80$	−8.89898	−	0.898979i	−0.994936	−	0.100509i
$81$	7.28115	+	5.29007i	0.809017	+	0.587785i
$82$		0			0
$83$	−5.53525	+	0.876698i	−0.607573	+	0.0962301i	−0.452638	−	0.891695i	$-0.649517\pi$
$83$	−5.53525	+	0.876698i	−0.607573	+	0.0962301i	−0.154935	+	0.987925i	$0.549517\pi$
$84$	−14.9105	−	4.84471i	−1.62687	−	0.528601i
$85$		0			0
$86$		0			0
$87$	14.4272	−	7.35102i	1.54676	−	0.788113i
$88$	4.45270	+	8.73892i	0.474660	+	0.931572i
$89$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$89$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$90$	−7.97714	−	5.13471i	−0.840864	−	0.541246i
$91$		0			0
$92$		0			0
$93$	12.0530	−	12.0530i	1.24983	−	1.24983i
$94$		0			0
$95$		0			0
$96$	−7.92672	+	5.75910i	−0.809017	+	0.587785i
$97$	−4.97879	−	0.788563i	−0.505520	−	0.0800665i	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−4.97879	−	0.788563i	−0.505520	−	0.0800665i	−0.403985	+	0.914766i	$0.632375\pi$
$98$	16.9894	+	8.65651i	1.71618	+	0.874439i
$99$			10.4029i			1.04553i
$100$	8.70038	+	4.92985i	0.870038	+	0.492985i
$101$	5.90202			0.587273			0.293636	−	0.955917i	$-0.405135\pi$
$101$	5.90202			0.587273			0.293636	+	0.955917i	$0.405135\pi$
$102$		0			0
$103$	2.52278	−	15.9282i	0.248577	−	1.56945i	−0.475489	−	0.879721i	$-0.657729\pi$
$103$	2.52278	−	15.9282i	0.248577	−	1.56945i	0.724066	−	0.689730i	$-0.242271\pi$
$104$		0			0
$105$	13.0734	+	11.6760i	1.27583	+	1.13946i
$106$	16.6132	+	12.0702i	1.61361	+	1.17236i
$107$	14.1202	+	14.1202i	1.36505	+	1.36505i	0.867353	+	0.497694i	$0.165820\pi$
$107$	14.1202	+	14.1202i	1.36505	+	1.36505i	0.497694	+	0.867353i	$0.334180\pi$
$108$	−10.2644	+	1.62571i	−0.987688	+	0.156434i
$109$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$109$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$110$	−0.618139	−	10.9482i	−0.0589372	−	1.04387i
$111$		0			0
$112$	16.1301	−	8.21867i	1.52415	−	0.776592i
$113$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$113$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$114$		0			0
$115$		0			0
$116$	−5.77767	+	17.7818i	−0.536443	+	1.65100i
$117$		0			0
$118$	14.3959	−	14.3959i	1.32525	−	1.32525i
$119$		0			0
$120$	10.7058	−	2.32084i	0.977299	−	0.211862i
$121$	−0.828775	+	0.602140i	−0.0753432	+	0.0547400i
$122$		0			0
$123$		0			0
$124$			19.6824i			1.76753i
$125$	−6.68080	−	8.96476i	−0.597549	−	0.801832i
$126$	19.2013			1.71059
$127$	−6.51604	+	12.7885i	−0.578205	+	1.13479i	0.397887	+	0.917434i	$0.369744\pi$
$127$	−6.51604	+	12.7885i	−0.578205	+	1.13479i	−0.976092	+	0.217357i	$0.930256\pi$
$128$	1.76985	−	11.1744i	0.156434	−	0.987688i
$129$		0			0
$130$		0			0
$131$	−10.9626	−	7.96479i	−0.957806	−	0.695887i	−0.00516600	−	0.999987i	$-0.501644\pi$
$131$	−10.9626	−	7.96479i	−0.957806	−	0.695887i	−0.952640	+	0.304100i	$0.901644\pi$
$132$	−8.49391	−	8.49391i	−0.739300	−	0.739300i
$133$		0			0
$134$		0			0
$135$	11.2351	+	2.96183i	0.966964	+	0.254914i
$136$		0			0
$137$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$137$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$138$		0			0
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$	−20.2078	+	1.14094i	−1.70787	+	0.0964273i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	7.05342	−	9.70820i	0.587785	−	0.809017i
$145$	13.9245	−	15.5910i	1.15637	−	1.29476i
$146$	3.39952	−	2.46990i	0.281346	−	0.204410i
$147$	−23.0654	−	3.65321i	−1.90240	−	0.301311i
$148$		0			0
$149$		−	22.8898i		−	1.87521i	−0.347704	−	0.937604i	$-0.613039\pi$
$149$		−	22.8898i		−	1.87521i	0.347704	−	0.937604i	$-0.386961\pi$
$150$	−12.0000	−	2.44949i	−0.979796	−	0.200000i
$151$	−16.0158			−1.30335			−0.651673	−	0.758500i	$-0.725932\pi$
$151$	−16.0158			−1.30335			−0.651673	+	0.758500i	$0.725932\pi$
$152$		0			0
$153$		0			0
$154$	13.0455	+	17.9556i	1.05124	+	1.44690i
$155$	8.86918	−	20.1391i	0.712390	−	1.61761i
$156$		0			0
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$	−19.6281	+	3.10879i	−1.56153	+	0.247322i
$159$	−23.9192	−	7.77182i	−1.89692	−	0.616345i
$160$	−6.84628	+	10.6362i	−0.541246	+	0.840864i
$161$		0			0
$162$	11.3407	−	5.77836i	0.891007	−	0.453990i
$163$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$163$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$164$		0			0
$165$	4.86352	+	12.5185i	0.378625	+	0.974563i
$166$	−2.44915	+	7.53770i	−0.190091	+	0.585039i
$167$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$167$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$168$	−15.6778	+	15.6778i	−1.20957	+	1.20957i
$169$	−7.64121	+	10.5172i	−0.587785	+	0.809017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.20079	−	2.64993i	−0.395409	−	0.201471i	0.244969	−	0.969531i	$-0.421222\pi$
$173$	−5.20079	−	2.64993i	−0.395409	−	0.201471i	−0.640378	+	0.768060i	$0.721222\pi$
$174$		−	22.8990i		−	1.73597i
$175$	21.1908	+	7.93851i	1.60188	+	0.600095i
$176$	13.8705			1.04553
$177$	−11.3200	+	22.2168i	−0.850865	+	1.66992i
$178$		0			0
$179$	−8.79782	−	12.1092i	−0.657580	−	0.905082i	0.341818	−	0.939766i	$-0.388957\pi$
$179$	−8.79782	−	12.1092i	−0.657580	−	0.905082i	−0.999398	+	0.0346846i	$0.988957\pi$
$180$	−11.5917	+	6.75510i	−0.863998	+	0.503495i
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−7.44915	−	22.9261i	−0.546198	−	1.68102i
$187$		0			0
$188$		0			0
$189$	−22.3657	+	7.26707i	−1.62687	+	0.528601i
$190$		0			0
$191$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$191$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$192$	2.16762	+	13.6858i	0.156434	+	0.987688i
$193$	19.2422	−	19.2422i	1.38509	−	1.38509i	0.549772	−	0.835315i	$-0.314715\pi$
$193$	19.2422	−	19.2422i	1.38509	−	1.38509i	0.835315	−	0.549772i	$-0.185285\pi$
$194$	−4.19023	+	5.76736i	−0.300841	+	0.414072i
$195$		0			0
$196$	21.8157	−	15.8500i	1.55826	−	1.13214i
$197$	27.5863	+	4.36924i	1.96544	+	0.311295i	0.998390	+	0.0567145i	$0.0180625\pi$
$197$	27.5863	+	4.36924i	1.96544	+	0.311295i	0.967051	+	0.254581i	$0.0819375\pi$
$198$	13.1084	+	6.67906i	0.931572	+	0.474660i
$199$		−	18.9698i		−	1.34473i	−0.740218	−	0.672367i	$-0.765278\pi$
$199$		−	18.9698i		−	1.34473i	0.740218	−	0.672367i	$-0.234722\pi$
$200$	11.7980	−	7.79796i	0.834242	−	0.551399i
$201$		0			0
$202$	3.78933	−	7.43697i	0.266616	−	0.523264i
$203$	−6.61863	+	41.7884i	−0.464537	+	2.93297i
$204$		0			0
$205$		0			0
$206$	−18.4510	−	13.4054i	−1.28554	−	0.934000i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	23.1063	−	8.97695i	1.59448	−	0.619469i
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$	25.8756	−	13.1843i	1.77714	−	0.905500i
$213$		0			0
$214$	26.8581	−	8.72673i	1.83598	−	0.596547i
$215$		0			0
$216$	−4.54160	+	13.9776i	−0.309017	+	0.951057i
$217$	6.96748	+	43.9910i	0.472984	+	2.98630i
$218$		0			0
$219$	−3.02499	+	4.16355i	−0.204410	+	0.281346i
$220$	−14.1924	−	6.25025i	−0.956848	−	0.421392i
$221$		0			0
$222$		0			0
$223$	−26.5862	−	13.5464i	−1.78035	−	0.907132i	−0.909802	−	0.415042i	$-0.863767\pi$
$223$	−26.5862	−	13.5464i	−1.78035	−	0.907132i	−0.870544	−	0.492090i	$-0.836233\pi$
$224$		−	25.6018i		−	1.71059i
$225$	14.9047	−	1.68843i	0.993645	−	0.112562i
$226$		0			0
$227$	−10.7544	+	21.1066i	−0.713793	+	1.40090i	0.193798	+	0.981041i	$0.437919\pi$
$227$	−10.7544	+	21.1066i	−0.713793	+	1.40090i	−0.907591	+	0.419856i	$0.862081\pi$
$228$		0			0
$229$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$229$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$230$		0			0
$231$	−21.9910	−	15.9774i	−1.44690	−	1.05124i
$232$	18.6969	+	18.6969i	1.22751	+	1.22751i
$233$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$233$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$234$		0			0
$235$		0			0
$236$	−8.89717	−	27.3827i	−0.579157	−	1.78246i
$237$	21.6863	−	11.0497i	1.40867	−	0.717756i
$238$		0			0
$239$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$239$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$240$	3.94911	−	14.9801i	0.254914	−	0.966964i
$241$	9.16483	−	28.2064i	0.590358	−	1.81694i	0.0137643	−	0.999905i	$-0.495619\pi$
$241$	9.16483	−	28.2064i	0.590358	−	1.81694i	0.576594	−	0.817031i	$-0.304381\pi$
$242$	0.226635	+	1.43091i	0.0145686	+	0.0919827i
$243$	−11.0227	+	11.0227i	−0.707107	+	0.707107i
$244$		0			0
$245$	−29.4641	+	6.38734i	−1.88239	+	0.408072i
$246$		0			0
$247$		0			0
$248$	24.8013	+	12.6369i	1.57488	+	0.802443i
$249$		−	9.70684i		−	0.615146i
$250$	−15.5856	+	2.66257i	−0.985719	+	0.168396i
$251$	0.710065			0.0448189			0.0224095	−	0.999749i	$-0.492866\pi$
$251$	0.710065			0.0448189			0.0224095	+	0.999749i	$0.492866\pi$
$252$	12.3280	−	24.1951i	0.776592	−	1.52415i
$253$		0			0
$254$	11.9308	+	16.4214i	0.748607	+	1.03037i
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$257$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	8.66651	+	26.6728i	0.536443	+	1.65100i
$262$	−17.0746	+	8.69996i	−1.05487	+	0.537486i
$263$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$263$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$264$	−16.1564	+	5.24953i	−0.994356	+	0.323086i
$265$	−32.4171	+	1.83028i	−1.99136	+	0.112434i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.89405	+	12.2416i	−0.542280	+	0.746384i	−0.988939	−	0.148320i	$-0.952613\pi$
$269$	−8.89405	+	12.2416i	−0.542280	+	0.746384i	0.446660	+	0.894704i	$0.352613\pi$
$270$	10.9455	−	12.2554i	0.666122	−	0.745843i
$271$	26.0472	−	18.9244i	1.58225	−	1.14958i	0.668202	−	0.743980i	$-0.267064\pi$
$271$	26.0472	−	18.9244i	1.58225	−	1.14958i	0.914052	−	0.405596i	$-0.132936\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.7052	+	12.7906i	0.705851	+	0.771300i
$276$		0			0
$277$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$277$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$278$		0			0
$279$	17.3536	+	23.8851i	1.03893	+	1.42996i
$280$	−11.5365	+	26.1958i	−0.689439	+	1.56550i
$281$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$281$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$282$		0			0
$283$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$283$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−7.70447	−	15.1209i	−0.453990	−	0.891007i
$289$	−16.1680	+	5.25329i	−0.951057	+	0.309017i
$290$	−10.7057	−	27.5559i	−0.628659	−	1.61814i
$291$	2.69803	−	8.30369i	0.158161	−	0.486771i
$292$	−0.929625	−	5.86942i	−0.0544022	−	0.343482i
$293$	2.69816	−	2.69816i	0.157628	−	0.157628i	−0.623887	−	0.781515i	$-0.714447\pi$
$293$	2.69816	−	2.69816i	0.157628	−	0.157628i	0.781515	+	0.623887i	$0.214447\pi$
$294$	−19.4122	+	26.7186i	−1.13214	+	1.55826i
$295$	−3.23541	+	32.0273i	−0.188373	+	1.86470i
$296$		0			0
$297$	−17.7965	−	2.81868i	−1.03266	−	0.163557i
$298$	−28.8429	−	14.6962i	−1.67082	−	0.851327i
$299$		0			0
$300$	−10.7910	+	13.5482i	−0.623019	+	0.782206i
$301$		0			0
$302$	−10.2828	+	20.1811i	−0.591706	+	1.16129i
$303$	−1.59917	+	10.0967i	−0.0918697	+	0.580042i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	31.0011	−	4.91009i	1.76645	−	0.279778i
$309$	26.5652	+	8.63157i	1.51124	+	0.491033i
$310$	−19.6824	−	24.1059i	−1.11789	−	1.36913i
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$		0			0
$313$	−15.7727	−	30.9557i	−0.891527	−	1.74972i	−0.614620	−	0.788823i	$-0.710691\pi$
$313$	−15.7727	−	30.9557i	−0.891527	−	1.74972i	−0.276907	−	0.960897i	$-0.589309\pi$
$314$		0			0
$315$	−23.5167	+	19.2013i	−1.32502	+	1.08187i
$316$	−8.68472	+	26.7288i	−0.488554	+	1.50361i
$317$	−1.07289	−	6.77399i	−0.0602598	−	0.380465i	−0.999325	−	0.0367271i	$-0.988307\pi$
$317$	−1.07289	−	6.77399i	−0.0602598	−	0.380465i	0.939066	−	0.343738i	$-0.111693\pi$
$318$	−25.1501	+	25.1501i	−1.41035	+	1.41035i
$319$	−19.0542	+	26.2259i	−1.06683	+	1.46837i
$320$	9.00680	+	15.4557i	0.503495	+	0.863998i
$321$	−27.9816	+	20.3298i	−1.56178	+	1.13470i
$322$		0			0
$323$		0			0
$324$		−	18.0000i		−	1.00000i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	18.8968	+	1.90896i	1.04023	+	0.105085i
$331$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$331$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$332$	7.92560	+	7.92560i	0.434974	+	0.434974i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	9.68942	+	29.8210i	0.528601	+	1.62687i
$337$	15.2638	−	7.77728i	0.831470	−	0.423655i	0.0141927	−	0.999899i	$-0.495482\pi$
$337$	15.2638	−	7.77728i	0.831470	−	0.423655i	0.817278	+	0.576244i	$0.195482\pi$
$338$	8.34651	+	16.3810i	0.453990	+	0.891007i
$339$		0			0
$340$		0			0
$341$	−10.5454	+	32.4554i	−0.571065	+	1.75756i
$342$		0			0
$343$	20.7465	−	20.7465i	1.12020	−	1.12020i
$344$		0			0
$345$		0			0
$346$	−6.67822	+	4.85201i	−0.359023	+	0.260846i
$347$	−33.9698	−	5.38028i	−1.82359	−	0.288829i	−0.851661	−	0.524093i	$-0.824404\pi$
$347$	−33.9698	−	5.38028i	−1.82359	−	0.288829i	−0.971931	+	0.235264i	$0.924404\pi$
$348$	−28.8544	−	14.7020i	−1.54676	−	0.788113i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	23.6084	−	21.6052i	1.26192	−	1.15484i
$351$		0			0
$352$	8.90541	−	17.4778i	0.474660	−	0.931572i
$353$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$353$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$354$	20.7269	+	28.5281i	1.10162	+	1.51625i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−20.9070	+	3.31134i	−1.10497	+	0.175010i
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$	1.06956	+	18.9435i	0.0563708	+	0.998410i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$		0			0
$363$	−0.805538	−	1.58096i	−0.0422798	−	0.0829788i
$364$		0			0
$365$	−1.69365	+	6.42452i	−0.0886497	+	0.336275i
$366$		0			0
$367$	5.99121	+	37.8270i	0.312739	+	1.97455i	0.184876	+	0.982762i	$0.440812\pi$
$367$	5.99121	+	37.8270i	0.312739	+	1.97455i	0.127862	+	0.991792i	$0.459188\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	53.1658	−	38.6272i	2.76023	−	2.00542i
$372$	−33.6712	−	5.33300i	−1.74577	−	0.276503i
$373$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$373$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$374$		0			0
$375$	17.1464	−	9.00000i	0.885438	−	0.464758i
$376$		0			0
$377$		0			0
$378$	−5.20265	+	32.8482i	−0.267595	+	1.68953i
$379$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$379$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$380$		0			0
$381$	−20.1120	−	14.6122i	−1.03037	−	0.748607i
$382$		0			0
$383$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$383$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$384$	18.6368	+	6.05547i	0.951057	+	0.309017i
$385$	−33.9330	−	8.94552i	−1.72939	−	0.455906i
$386$	−11.8924	−	36.6009i	−0.605305	−	1.86294i
$387$		0			0
$388$	4.57700	+	8.98287i	0.232362	+	0.456036i
$389$	−36.8347	+	11.9683i	−1.86759	+	0.606818i	−0.875192	+	0.483775i	$0.839265\pi$
$389$	−36.8347	+	11.9683i	−1.86759	+	0.606818i	−0.992401	+	0.123043i	$0.960735\pi$
$390$		0			0
$391$		0			0
$392$	−5.96566	−	37.6657i	−0.301311	−	1.90240i
$393$	16.5959	−	16.5959i	0.837153	−	0.837153i
$394$	23.2171	−	31.9555i	1.16966	−	1.60990i
$395$	20.9306	−	23.4356i	1.05313	−	1.17917i
$396$	16.8322	−	12.2293i	0.845850	−	0.614546i
$397$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$397$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$398$	−23.9033	−	12.1794i	−1.19817	−	0.610496i
$399$		0			0
$400$	−2.25125	−	19.8729i	−0.112562	−	0.993645i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	−6.93824	−	9.54966i	−0.345190	−	0.475113i
$405$	−8.11106	+	18.4177i	−0.403042	+	0.915182i
$406$	48.4070	+	35.1697i	2.40240	+	1.74544i
$407$		0			0
$408$		0			0
$409$	20.5633	+	6.68141i	1.01679	+	0.330375i	0.769554	−	0.638581i	$-0.220478\pi$
$409$	20.5633	+	6.68141i	1.01679	+	0.330375i	0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$		0			0
$412$	−28.7381	+	14.6428i	−1.41582	+	0.721398i
$413$	−29.5789	−	58.0518i	−1.45548	−	2.85654i
$414$		0			0
$415$	−4.53812	−	11.6809i	−0.222767	−	0.573393i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.39221	+	3.29259i	−0.116867	+	0.160854i	−0.863443	−	0.504447i	$-0.831697\pi$
$419$	−2.39221	+	3.29259i	−0.116867	+	0.160854i	0.746576	+	0.665300i	$0.231697\pi$
$420$	3.52351	−	34.8791i	0.171930	−	1.70193i
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$		0			0
$424$		−	41.0700i		−	1.99454i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	6.24765	−	39.4461i	0.301992	−	1.90670i
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$	14.6969	+	14.6969i	0.707107	+	0.707107i
$433$	5.25315	−	0.832017i	0.252450	−	0.0399842i	−0.0289266	−	0.999582i	$-0.509209\pi$
$433$	5.25315	−	0.832017i	0.252450	−	0.0399842i	0.281377	+	0.959597i	$0.409209\pi$
$434$	59.9052	+	19.4644i	2.87554	+	0.934321i
$435$	22.8990	+	28.0454i	1.09792	+	1.34467i
$436$		0			0
$437$		0			0
$438$	3.30421	+	6.48488i	0.157881	+	0.309859i
$439$	12.1635	−	3.95216i	0.580532	−	0.188626i	−0.00400696	−	0.999992i	$-0.501275\pi$
$439$	12.1635	−	3.95216i	0.580532	−	0.188626i	0.584539	+	0.811366i	$0.301275\pi$
$440$	−16.9878	+	13.8705i	−0.809863	+	0.661250i
$441$	12.4993	−	38.4688i	0.595203	−	1.83185i
$442$		0			0
$443$	29.5908	−	29.5908i	1.40590	−	1.40590i	0.626401	−	0.779501i	$-0.284527\pi$
$443$	29.5908	−	29.5908i	1.40590	−	1.40590i	0.779501	−	0.626401i	$-0.215473\pi$
$444$		0			0
$445$		0			0
$446$	−34.1388	+	24.8033i	−1.61652	+	1.17447i
$447$	39.1583	+	6.20206i	1.85212	+	0.293347i
$448$	−32.2601	−	16.4373i	−1.52415	−	0.776592i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	7.44184	−	19.8650i	0.350812	−	0.936446i
$451$		0			0
$452$		0			0
$453$	4.33951	−	27.3986i	0.203888	−	1.28730i
$454$	19.6912	+	27.1026i	0.924153	+	1.27199i
$455$		0			0
$456$		0			0
$457$	−24.5449	−	24.5449i	−1.14816	−	1.14816i	−0.986914	−	0.161248i	$-0.948448\pi$
$457$	−24.5449	−	24.5449i	−1.14816	−	1.14816i	−0.161248	−	0.986914i	$-0.551552\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.5873	+	38.7396i	0.586247	+	1.80428i	0.594204	+	0.804315i	$0.297467\pi$
$461$	12.5873	+	38.7396i	0.586247	+	1.80428i	−0.00795653	+	0.999968i	$0.502533\pi$
$462$	−34.2518	+	17.4522i	−1.59354	+	0.811948i
$463$	19.3552	+	37.9867i	0.899512	+	1.76539i	0.571165	+	0.820835i	$0.306492\pi$
$463$	19.3552	+	37.9867i	0.899512	+	1.76539i	0.328348	+	0.944557i	$0.393508\pi$
$464$	35.5637	−	11.5553i	1.65100	−	0.536443i
$465$	32.0494	+	20.6295i	1.48626	+	0.956670i
$466$		0			0
$467$	−4.49111	−	28.3558i	−0.207824	−	1.31215i	−0.842217	−	0.539138i	$-0.818750\pi$
$467$	−4.49111	−	28.3558i	−0.207824	−	1.31215i	0.634393	−	0.773010i	$-0.281250\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−40.2165	−	6.36967i	−1.85112	−	0.293188i
$473$		0			0
$474$		−	34.4206i		−	1.58099i
$475$		0			0
$476$		0			0
$477$	19.7764	−	38.8134i	0.905500	−	1.77714i
$478$		0			0
$479$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$479$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$480$	−16.3406	−	14.5940i	−0.745843	−	0.666122i
$481$		0			0
$482$	−29.6580	−	29.6580i	−1.35088	−	1.35088i
$483$		0			0
$484$	1.94857	+	0.633128i	0.0885712	+	0.0287785i
$485$	−0.635394	−	11.2538i	−0.0288518	−	0.511007i
$486$	6.81241	+	20.9664i	0.309017	+	0.951057i
$487$	−34.1944	+	17.4229i	−1.54949	+	0.789507i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$	−34.1944	+	17.4229i	−1.54949	+	0.789507i	−0.550521	+	0.834821i	$0.685571\pi$
$488$		0			0
$489$		0			0
$490$	−10.8686	+	41.2279i	−0.490994	+	1.86249i
$491$	−5.06413	+	15.5858i	−0.228541	+	0.703377i	0.769372	+	0.638801i	$0.220569\pi$
$491$	−5.06413	+	15.5858i	−0.228541	+	0.703377i	−0.997913	+	0.0645759i	$0.979431\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−22.7335	+	4.92825i	−1.02179	+	0.221508i
$496$	31.8468	−	23.1381i	1.42996	−	1.03893i
$497$		0			0
$498$	−12.2313	−	6.23218i	−0.548099	−	0.279271i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−6.65153	+	21.3485i	−0.297465	+	0.954733i
$501$		0			0
$502$	0.455890	−	0.894734i	0.0203474	−	0.0399339i
$503$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$503$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$504$	−22.5725	−	31.0684i	−1.00546	−	1.38390i
$505$	2.79601	+	12.8977i	0.124421	+	0.573941i
$506$		0			0
$507$	−15.9217	−	15.9217i	−0.707107	−	0.707107i
$508$	28.3522	−	4.49055i	1.25793	−	0.199236i
$509$	−17.0473	−	5.53899i	−0.755607	−	0.245511i	−0.0942147	−	0.995552i	$-0.530034\pi$
$509$	−17.0473	−	5.53899i	−0.755607	−	0.245511i	−0.661392	+	0.750040i	$0.730034\pi$
$510$		0			0
$511$	−4.15549	−	12.7893i	−0.183828	−	0.565765i
$512$	−20.1612	+	10.2726i	−0.891007	+	0.453990i
$513$		0			0
$514$		0			0
$515$	36.0032	−	2.03276i	1.58649	−	0.0895740i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	5.94248	−	8.17912i	0.260846	−	0.359023i
$520$		0			0
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$	39.1739	+	6.20453i	1.71459	+	0.271565i
$523$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$523$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$524$			27.1010i			1.18391i
$525$	−19.3223	+	34.1007i	−0.843295	+	1.48828i
$526$		0			0
$527$		0			0
$528$	−3.75825	+	23.7286i	−0.163557	+	1.03266i
$529$	13.5191	+	18.6074i	0.587785	+	0.809017i
$530$	−18.5067	+	42.0230i	−0.803881	+	1.82536i
$531$	−34.9397	−	25.3851i	−1.51625	−	1.10162i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−24.1676	+	37.5461i	−1.04486	+	1.62326i
$536$		0			0
$537$	23.0993	−	11.7697i	0.996807	−	0.507898i
$538$	9.71499	+	19.0667i	0.418843	+	0.822026i
$539$	44.4651	−	14.4476i	1.91525	−	0.622302i
$540$	−8.41531	−	21.6606i	−0.362137	−	0.932125i
$541$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$541$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$542$	−7.12280	−	44.9716i	−0.305951	−	1.93170i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$547$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$548$		0			0
$549$		0			0
$550$	23.6323	−	6.53739i	1.00768	−	0.278755i
$551$		0			0
$552$		0			0
$553$	−9.94880	+	62.8143i	−0.423066	+	2.67113i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.8840	+	19.8840i	0.842511	+	0.842511i	0.989185	−	0.146674i	$-0.0468568\pi$
$557$	19.8840	+	19.8840i	0.842511	+	0.842511i	−0.146674	+	0.989185i	$0.546857\pi$
$558$	41.2387	−	6.53156i	1.74577	−	0.276503i
$559$		0			0
$560$	25.6018	+	31.3556i	1.08187	+	1.32502i
$561$		0			0
$562$		0			0
$563$	6.44785	+	12.6546i	0.271744	+	0.533329i	0.986039	−	0.166517i	$-0.0532521\pi$
$563$	6.44785	+	12.6546i	0.271744	+	0.533329i	−0.714294	+	0.699846i	$0.753252\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−6.37191	−	40.2307i	−0.267595	−	1.68953i
$568$		0			0
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$571$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−24.0000			−1.00000
$577$	15.8790	−	31.1643i	0.661051	−	1.29739i	−0.280285	−	0.959917i	$-0.590429\pi$
$577$	15.8790	−	31.1643i	0.661051	−	1.29739i	0.941336	−	0.337470i	$-0.109571\pi$
$578$	−3.76094	+	23.7456i	−0.156434	+	0.987688i
$579$	27.7045	+	38.1319i	1.15136	+	1.58471i
$580$	−41.5959	−	4.20204i	−1.72718	−	0.174480i
$581$	20.5197	+	14.9084i	0.851299	+	0.618505i
$582$	−8.73101	−	8.73101i	−0.361912	−	0.361912i
$583$	49.7315	−	7.87670i	2.05967	−	0.326220i
$584$	−7.99276	−	2.59700i	−0.330743	−	0.107465i
$585$		0			0
$586$	−1.66755	−	5.13220i	−0.0688860	−	0.212009i
$587$	2.21706	−	1.12965i	0.0915080	−	0.0466257i	−0.407638	−	0.913144i	$-0.633647\pi$
$587$	2.21706	−	1.12965i	0.0915080	−	0.0466257i	0.499146	+	0.866518i	$0.333647\pi$
$588$	21.2040	+	41.6153i	0.874439	+	1.71618i
$589$		0			0
$590$	38.2794	+	24.6396i	1.57594	+	1.01440i
$591$	−14.9491	+	46.0087i	−0.614926	+	1.89255i
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$	−14.9778	+	20.6152i	−0.614546	+	0.845850i
$595$		0			0
$596$	−37.0365	+	26.9086i	−1.51708	+	1.10222i
$597$	32.4521	+	5.13991i	1.32818	+	0.210363i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	10.1435	+	22.2960i	0.414106	+	0.910229i
$601$	47.2101			1.92574			0.962870	−	0.269965i	$-0.0870123\pi$
$601$	47.2101			1.92574			0.962870	+	0.269965i	$0.0870123\pi$
$602$		0			0
$603$		0			0
$604$	18.8277	+	25.9141i	0.766087	+	1.05443i
$605$	−1.70848	−	1.52587i	−0.0694598	−	0.0620355i
$606$	11.6959	+	8.49757i	0.475113	+	0.345190i
$607$	0.293214	+	0.293214i	0.0119012	+	0.0119012i	0.713032	−	0.701131i	$-0.247321\pi$
$607$	0.293214	+	0.293214i	0.0119012	+	0.0119012i	−0.701131	+	0.713032i	$0.747321\pi$
$608$		0			0
$609$	−69.6951	−	22.6453i	−2.82419	−	0.917635i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$613$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$614$		0			0
$615$		0			0
$616$	13.7169	−	42.2161i	0.552668	−	1.70094i
$617$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$617$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$618$	27.9323	−	27.9323i	1.12360	−	1.12360i
$619$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$619$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$620$	−43.0122	+	9.32433i	−1.72741	+	0.374474i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	16.4258	−	18.8466i	0.657032	−	0.753863i
$626$	−49.1332			−1.96376
$627$		0			0
$628$		0			0
$629$		0			0
$630$	9.09642	+	41.9608i	0.362410	+	1.67176i
$631$	3.96336	+	2.87955i	0.157779	+	0.114633i	0.663873	−	0.747845i	$-0.268911\pi$
$631$	3.96336	+	2.87955i	0.157779	+	0.114633i	−0.506095	+	0.862478i	$0.668911\pi$
$632$	28.1043	+	28.1043i	1.11793	+	1.11793i
$633$		0			0
$634$	−9.22457	−	2.99724i	−0.366354	−	0.119036i
$635$	−31.0336	−	8.18117i	−1.23153	−	0.324660i
$636$	15.5436	+	47.8384i	0.616345	+	1.89692i
$637$		0			0
$638$	20.8130	+	40.8478i	0.823994	+	1.61718i
$639$		0			0
$640$	25.2580	−	1.42608i	0.998410	−	0.0563708i
$641$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$641$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$642$	7.65178	+	48.3114i	0.301992	+	1.90670i
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$647$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$648$	−22.6813	−	11.5567i	−0.891007	−	0.453990i
$649$		−	49.9197i		−	1.95952i
$650$		0			0
$651$	−77.1443			−3.02353
$652$		0			0
$653$	4.49271	−	28.3659i	0.175813	−	1.11004i	−0.729088	−	0.684420i	$-0.760055\pi$
$653$	4.49271	−	28.3659i	0.175813	−	1.11004i	0.904901	−	0.425622i	$-0.139945\pi$
$654$		0			0
$655$	12.2121	−	27.7299i	0.477167	−	1.08350i
$656$		0			0
$657$	−6.30306	−	6.30306i	−0.245906	−	0.245906i
$658$		0			0
$659$	16.0450	+	5.21335i	0.625026	+	0.203083i	0.604371	−	0.796703i	$-0.293425\pi$
$659$	16.0450	+	5.21335i	0.625026	+	0.203083i	0.0206555	+	0.999787i	$0.493425\pi$
$660$	14.5379	−	22.5857i	0.565888	−	0.879148i
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$		0			0
$663$		0			0
$664$	15.0754	−	4.89829i	0.585039	−	0.190091i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	30.3777	−	41.8114i	1.17447	−	1.61652i
$670$		0			0
$671$		0			0
$672$	43.7976	+	6.93686i	1.68953	+	0.267595i
$673$	−39.2293	−	19.9883i	−1.51218	−	0.770494i	−0.515897	−	0.856650i	$-0.672541\pi$
$673$	−39.2293	−	19.9883i	−1.51218	−	0.770494i	−0.996282	+	0.0861567i	$0.972541\pi$
$674$		−	24.2268i		−	0.933181i
$675$	−1.15001	+	25.9553i	−0.0442638	+	0.999020i
$676$	26.0000			1.00000
$677$	12.8270	−	25.1745i	0.492983	−	0.967534i	−0.501748	−	0.865014i	$-0.667310\pi$
$677$	12.8270	−	25.1745i	0.492983	−	0.967534i	0.994731	−	0.102520i	$-0.0326905\pi$
$678$		0			0
$679$	13.4097	+	18.4568i	0.514615	+	0.708307i
$680$		0			0
$681$	−33.1938	−	24.1167i	−1.27199	−	0.924153i
$682$	34.1256	+	34.1256i	1.30674	+	1.30674i
$683$	−50.5365	+	8.00419i	−1.93372	+	0.306272i	−0.998817	−	0.0486213i	$-0.984517\pi$
$683$	−50.5365	+	8.00419i	−1.93372	+	0.306272i	−0.934907	+	0.354893i	$0.884517\pi$
$684$		0			0
$685$		0			0
$686$	−12.8220	−	39.4622i	−0.489548	−	1.50667i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$691$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$692$	1.82621	+	11.5302i	0.0694221	+	0.438314i
$693$	33.2915	−	33.2915i	1.26464	−	1.26464i
$694$	−28.5895	+	39.3500i	−1.08524	+	1.49371i
$695$		0			0
$696$	−37.0513	+	26.9194i	−1.40443	+	1.02038i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−12.0665	−	43.6197i	−0.456072	−	1.64867i
$701$	−0.944387			−0.0356690			−0.0178345	−	0.999841i	$-0.505677\pi$
$701$	−0.944387			−0.0356690			−0.0178345	+	0.999841i	$0.505677\pi$
$702$		0			0
$703$		0			0
$704$	−16.3057	−	22.4429i	−0.614546	−	0.845850i
$705$		0			0
$706$		0			0
$707$	−18.8878	−	18.8878i	−0.710347	−	0.710347i
$708$	49.2550	−	7.80122i	1.85112	−	0.293188i
$709$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$709$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$710$		0			0
$711$	13.0271	+	40.0932i	0.488554	+	1.50361i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−9.25058	+	28.4704i	−0.345710	+	1.06399i
$717$		0			0
$718$		0			0
$719$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$719$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$720$	24.5569	+	10.8147i	0.915182	+	0.403042i
$721$	−59.0472	+	42.9003i	−2.19903	+	1.59769i
$722$	−26.5392	−	4.20340i	−0.987688	−	0.156434i
$723$	45.7703	+	23.3211i	1.70221	+	0.867321i
$724$		0			0
$725$	40.6676	+	23.0433i	1.51036	+	0.855806i
$726$	−2.50931			−0.0931293
$727$	−16.6573	+	32.6918i	−0.617786	+	1.21247i	0.344077	+	0.938941i	$0.388192\pi$
$727$	−16.6573	+	32.6918i	−0.617786	+	1.21247i	−0.961863	+	0.273532i	$0.911808\pi$
$728$		0			0
$729$	−15.8702	−	21.8435i	−0.587785	−	0.809017i
$730$	7.00797	+	6.25892i	0.259377	+	0.231653i
$731$		0			0
$732$		0			0
$733$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$733$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$734$	51.5114	+	16.7371i	1.90132	+	0.617777i
$735$	−2.94361	−	52.1357i	−0.108577	−	1.92306i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$	−14.5386	−	91.7930i	−0.533728	−	3.36983i
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$	−28.3382	+	39.0042i	−1.03893	+	1.42996i
$745$	50.0214	−	10.8438i	1.83264	−	0.397286i
$746$		0			0
$747$	16.6058	+	2.63009i	0.607573	+	0.0962301i
$748$		0			0
$749$		−	90.3752i		−	3.30224i
$750$	−0.331977	−	27.3841i	−0.0121221	−	0.999927i
$751$	49.4748			1.80536			0.902680	−	0.430312i	$-0.141596\pi$
$751$	49.4748			1.80536			0.902680	+	0.430312i	$0.141596\pi$
$752$		0			0
$753$	−0.192394	+	1.21473i	−0.00701122	+	0.0442671i
$754$		0			0
$755$	−7.58729	−	34.9994i	−0.276130	−	1.27376i
$756$	38.0509	+	27.6456i	1.38390	+	1.00546i
$757$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$757$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$761$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$762$	−31.3252	+	15.9610i	−1.13479	+	0.578205i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	19.5959	−	19.5959i	0.707107	−	0.707107i
$769$	−4.56182	+	6.27881i	−0.164504	+	0.226420i	−0.883309	−	0.468792i	$-0.844689\pi$
$769$	−4.56182	+	6.27881i	−0.164504	+	0.226420i	0.718805	+	0.695212i	$0.244689\pi$
$770$	−33.0583	+	37.0147i	−1.19134	+	1.33392i
$771$		0			0
$772$	−53.7552	−	8.51399i	−1.93469	−	0.306425i
$773$	49.4834	+	25.2131i	1.77980	+	0.906851i	0.912538	+	0.408993i	$0.134120\pi$
$773$	49.4834	+	25.2131i	1.77980	+	0.906851i	0.867258	+	0.497859i	$0.165880\pi$
$774$		0			0
$775$	48.2119	+	9.84121i	1.73182	+	0.353507i
$776$	14.2577			0.511821
$777$		0			0
$778$	−8.56837	+	54.0986i	−0.307191	+	1.93953i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−47.9780	+	7.59897i	−1.71459	+	0.271565i
$784$	−51.2917	−	16.6657i	−1.83185	−	0.595203i
$785$		0			0
$786$	−10.2568	−	31.5673i	−0.365849	−	1.12597i
$787$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$787$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$788$	−25.3601	−	49.7719i	−0.903414	−	1.77305i
$789$		0			0
$790$	−16.0922	−	41.4207i	−0.572537	−	1.47368i
$791$		0			0
$792$	−4.60289	−	29.0615i	−0.163557	−	1.03266i
$793$		0			0
$794$		0			0
$795$	5.65236	−	55.9526i	0.200469	−	1.98444i
$796$	−30.6938	+	22.3003i	−1.08791	+	0.790414i
$797$	−32.6721	−	5.17476i	−1.15731	−	0.183299i	−0.451877	−	0.892080i	$-0.649246\pi$
$797$	−32.6721	−	5.17476i	−1.15731	−	0.183299i	−0.705429	+	0.708781i	$0.749246\pi$
$798$		0			0
$799$		0			0
$800$	−26.4867	−	9.92245i	−0.936446	−	0.350812i
$801$		0			0
$802$		0			0
$803$	1.61180	−	10.1765i	0.0568790	−	0.359120i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.5322	−	18.5322i	−0.652363	−	0.652363i
$808$	−16.4879	+	2.61143i	−0.580042	+	0.0918697i
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	18.0000	+	22.0454i	0.632456	+	0.774597i
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$	75.3957	−	38.4160i	2.64587	−	1.34814i
$813$	25.3169	+	49.6872i	0.887903	+	1.74261i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	21.6215	−	21.6215i	0.755978	−	0.755978i
$819$		0			0
$820$		0			0
$821$	18.8268	−	13.6785i	0.657060	−	0.477382i	−0.208609	−	0.977999i	$-0.566894\pi$
$821$	18.8268	−	13.6785i	0.657060	−	0.477382i	0.865669	+	0.500617i	$0.166894\pi$
$822$		0			0
$823$	−8.61745	−	4.39081i	−0.300386	−	0.153054i	0.297301	−	0.954784i	$-0.403913\pi$
$823$	−8.61745	−	4.39081i	−0.300386	−	0.153054i	−0.597687	+	0.801730i	$0.703913\pi$
$824$			45.6133i			1.58902i
$825$	−25.0527	+	16.5588i	−0.872223	+	0.576503i
$826$	−92.1403			−3.20597
$827$	−18.9122	+	37.1173i	−0.657642	+	1.29069i	0.285524	+	0.958372i	$0.407832\pi$
$827$	−18.9122	+	37.1173i	−0.657642	+	1.29069i	−0.943166	+	0.332323i	$0.892168\pi$
$828$		0			0
$829$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$829$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$830$	−17.6324	−	1.78124i	−0.612031	−	0.0618277i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−45.5629	+	23.2155i	−1.57488	+	0.802443i
$838$	2.61302	+	5.12833i	0.0902652	+	0.177155i
$839$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$839$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$840$	−41.6881	−	26.8337i	−1.43837	−	0.925850i
$841$	−18.0447	+	55.5359i	−0.622231	+	1.91503i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−26.6033	−	11.7160i	−0.915182	−	0.403042i
$846$		0			0
$847$	4.57924	+	0.725281i	0.157345	+	0.0249209i
$848$	−51.7512	−	26.3686i	−1.77714	−	0.905500i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$853$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$854$		0			0
$855$		0			0
$856$	−45.6938	−	33.1985i	−1.56178	−	1.13470i
$857$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$857$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$858$		0			0
$859$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$859$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$863$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$864$	27.9552	−	9.08321i	0.951057	−	0.309017i
$865$	3.32711	−	12.6207i	0.113125	−	0.429117i
$866$	2.32433	−	7.15354i	0.0789838	−	0.243087i
$867$	−4.60619	−	29.0823i	−0.156434	−	0.987688i
$868$	62.9881	−	62.9881i	2.13796	−	2.13796i
$869$	−28.6414	+	39.4215i	−0.971593	+	1.33728i
$870$	50.0413	−	10.8481i	1.69656	−	0.367786i
$871$		0			0
$872$		0			0
$873$	13.4743	+	6.86550i	0.456036	+	0.232362i
$874$		0			0
$875$	−7.30917	+	50.0692i	−0.247095	+	1.69265i
$876$	10.2929			0.347763
$877$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$877$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$878$	2.82943	−	17.8643i	0.0954887	−	0.602892i
$879$	3.88474	+	5.34689i	0.131029	+	0.180346i
$880$	6.57100	+	30.3113i	0.221508	+	1.02179i
$881$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$881$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$882$	−40.4485	−	40.4485i	−1.36197	−	1.36197i
$883$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$883$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$884$		0			0
$885$	−53.9132	−	14.2128i	−1.81227	−	0.477757i
$886$	−18.2881	−	56.2851i	−0.614402	−	1.89093i
$887$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$887$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$888$		0			0
$889$	61.7786	−	20.0731i	2.07199	−	0.673230i
$890$		0			0
$891$	9.64399	−	29.6812i	0.323086	−	0.994356i
$892$	9.33552	+	58.9422i	0.312576	+	1.97353i
$893$		0			0
$894$	32.9562	−	45.3603i	1.10222	−	1.51708i
$895$	22.2944	−	24.9625i	0.745219	−	0.834406i
$896$	−41.4245	+	30.0967i	−1.38390	+	1.00546i
$897$		0			0
$898$		0			0
$899$			92.0003i			3.06838i
$900$	−20.2534	−	22.1314i	−0.675114	−	0.737713i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−31.7381	−	23.0591i	−1.05443	−	0.766087i
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$	46.7938	−	7.41141i	1.55291	−	0.245956i
$909$	−16.8395	−	5.47147i	−0.558529	−	0.181477i
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$		0			0
$913$	8.82259	+	17.3153i	0.291985	+	0.573053i
$914$	−46.6872	+	15.1696i	−1.54427	+	0.501765i
$915$		0			0
$916$		0			0
$917$	9.59363	+	60.5718i	0.316810	+	2.00026i
$918$		0			0
$919$	−20.1568	+	27.7435i	−0.664913	+	0.915174i	−0.999632	−	0.0271443i	$-0.991359\pi$
$919$	−20.1568	+	27.7435i	−0.664913	+	0.915174i	0.334719	+	0.942318i	$0.391359\pi$
$920$		0			0
$921$		0			0
$922$	56.8963	+	9.01148i	1.87378	+	0.296777i
$923$		0			0
$924$			54.3648i			1.78847i
$925$		0			0
$926$	60.2929			1.98135
$927$	−21.9642	+	43.1071i	−0.721398	+	1.41582i
$928$	8.27271	−	52.2319i	0.271565	−	1.71459i
$929$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$929$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$930$	46.5717	−	27.1397i	1.52715	−	0.889945i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−38.6138	−	12.5464i	−1.26348	−	0.410531i
$935$		0			0
$936$		0			0
$937$	9.16085	−	4.66769i	0.299272	−	0.152487i	−0.297907	−	0.954595i	$-0.596288\pi$
$937$	9.16085	−	4.66769i	0.299272	−	0.152487i	0.597178	+	0.802108i	$0.296288\pi$
$938$		0			0
$939$	57.2304	−	18.5953i	1.86764	−	0.606834i
$940$		0			0
$941$	16.5176	−	50.8361i	0.538460	−	1.65721i	−0.197592	−	0.980284i	$-0.563312\pi$
$941$	16.5176	−	50.8361i	0.538460	−	1.65721i	0.736052	−	0.676925i	$-0.236688\pi$
$942$		0			0
$943$		0			0
$944$	−33.8469	+	46.5862i	−1.10162	+	1.51625i
$945$	−26.4763	−	45.4333i	−0.861274	−	1.47795i
$946$		0			0
$947$	−13.4647	−	2.13260i	−0.437544	−	0.0693001i	−0.0662232	−	0.997805i	$-0.521095\pi$
$947$	−13.4647	−	2.13260i	−0.437544	−	0.0693001i	−0.371321	+	0.928505i	$0.621095\pi$
$948$	−43.3725	−	22.0994i	−1.40867	−	0.717756i
$949$		0			0
$950$		0			0
$951$	11.8791			0.385208
$952$		0			0
$953$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$953$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$954$	−36.2105	−	49.8395i	−1.17236	−	1.61361i
$955$		0			0
$956$		0			0
$957$	−39.7025	−	39.7025i	−1.28340	−	1.28340i
$958$		0			0
$959$		0			0
$960$	−28.8808	+	11.2204i	−0.932125	+	0.362137i
$961$	20.3486	+	62.6265i	0.656406	+	2.02021i
$962$		0			0
$963$	−27.1971	−	53.3773i	−0.876414	−	1.72006i
$964$	−56.4129	+	18.3297i	−1.81694	+	0.590358i
$965$	51.1660	+	32.9344i	1.64709	+	1.06020i
$966$		0			0
$967$	−9.45964	−	59.7258i	−0.304202	−	1.92065i	−0.382972	−	0.923760i	$-0.625099\pi$
$967$	−9.45964	−	59.7258i	−0.304202	−	1.92065i	0.0787703	−	0.996893i	$-0.474901\pi$
$968$	2.04884	−	2.04884i	0.0658523	−	0.0658523i
$969$		0			0
$970$	−14.5885	−	6.42472i	−0.468409	−	0.206285i
$971$	−50.1600	+	36.4434i	−1.60971	+	1.16952i	−0.745318	+	0.666710i	$0.767702\pi$
$971$	−50.1600	+	36.4434i	−1.60971	+	1.16952i	−0.864394	+	0.502814i	$0.832298\pi$
$972$	30.7931	+	4.87714i	0.987688	+	0.156434i
$973$		0			0
$974$			54.2736i			1.73904i
$975$		0			0
$976$		0			0
$977$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$977$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$978$		0			0
$979$		0			0
$980$	44.9721	+	40.1652i	1.43658	+	1.28303i
$981$		0			0
$982$	16.3879	+	16.3879i	0.522958	+	0.522958i
$983$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$983$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$984$		0			0
$985$	3.52057	+	62.3544i	0.112175	+	1.98678i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−8.38584	+	31.8100i	−0.266520	+	1.01099i
$991$	10.0509	−	30.9333i	0.319276	−	0.982630i	−0.654683	−	0.755904i	$-0.727198\pi$
$991$	10.0509	−	30.9333i	0.319276	−	0.982630i	0.973959	−	0.226726i	$-0.0728023\pi$
$992$	−8.70875	−	54.9849i	−0.276503	−	1.74577i
$993$		0			0
$994$		0			0
$995$	41.4548	−	8.98673i	1.31421	−	0.284898i
$996$	−15.7060	+	11.4111i	−0.497664	+	0.361574i
$997$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$997$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bp.b.317.1	yes	16
3.2	odd	2		600.2.bp.a.317.2	yes	16
8.5	even	2		600.2.bp.a.317.2	yes	16
24.5	odd	2	CM	600.2.bp.b.317.1	yes	16
25.3	odd	20	inner	600.2.bp.b.53.1	yes	16
75.53	even	20		600.2.bp.a.53.2	✓	16
200.53	odd	20		600.2.bp.a.53.2	✓	16
600.53	even	20	inner	600.2.bp.b.53.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bp.a.53.2	✓	16	75.53	even	20
600.2.bp.a.53.2	✓	16	200.53	odd	20
600.2.bp.a.317.2	yes	16	3.2	odd	2
600.2.bp.a.317.2	yes	16	8.5	even	2
600.2.bp.b.53.1	yes	16	25.3	odd	20	inner
600.2.bp.b.53.1	yes	16	600.53	even	20	inner
600.2.bp.b.317.1	yes	16	1.1	even	1	trivial
600.2.bp.b.317.1	yes	16	24.5	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bp (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642040 - 1.26007i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(0.473739 + 2.18531i) q^{5} +(1.98168 + 1.43977i) q^{6} +(-3.20022 - 3.20022i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(3.05781 + 0.806108i) q^{10} +(-1.07155 - 3.29791i) q^{11} +(3.08654 - 1.57267i) q^{12} +(-6.08718 + 1.97785i) q^{14} +(-3.86682 + 0.218323i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-3.00000 + 3.00000i) q^{18} +(2.97899 - 3.33551i) q^{20} +(6.34181 - 4.60759i) q^{21} +(-4.84359 - 0.767149i) q^{22} -4.89898i q^{24} +(-4.55114 + 2.07053i) q^{25} +(2.35900 - 4.62981i) q^{27} +(-1.41598 + 8.94015i) q^{28} +(-5.49489 - 7.56307i) q^{29} +(-2.20755 + 5.01266i) q^{30} +(-7.96171 - 5.78452i) q^{31} +(4.00000 + 4.00000i) q^{32} +(5.93216 - 0.939561i) q^{33} +(5.47740 - 8.50954i) q^{35} +(1.85410 + 5.70634i) q^{36} +(-2.29036 - 5.89527i) q^{40} +(-1.73422 - 10.9494i) q^{42} +(-4.07644 + 5.61073i) q^{44} +(0.674235 - 6.67423i) q^{45} +(-6.17307 - 3.14534i) q^{48} +13.4828i q^{49} +(-0.312992 + 7.06414i) q^{50} +(-2.27150 + 14.3417i) q^{53} +(-4.31932 - 5.94504i) q^{54} +(6.69931 - 3.90402i) q^{55} +(10.3561 + 7.52417i) q^{56} +(-13.0580 + 2.06818i) q^{58} +(13.6913 + 4.44859i) q^{59} +(4.89898 + 6.00000i) q^{60} +(-12.4006 + 6.31845i) q^{62} +(6.16401 + 12.0975i) q^{63} +(7.60845 - 2.47214i) q^{64} +(2.62476 - 8.07819i) q^{66} +(-7.20594 - 12.3654i) q^{70} +(8.38081 + 1.32739i) q^{72} +(2.64744 + 1.34894i) q^{73} +(-2.30897 - 8.34678i) q^{75} +(-7.12482 + 13.9832i) q^{77} +(-8.25966 - 11.3684i) q^{79} +(-8.89898 - 0.898979i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-5.53525 + 0.876698i) q^{83} +(-14.9105 - 4.84471i) q^{84} +(14.4272 - 7.35102i) q^{87} +(4.45270 + 8.73892i) q^{88} +(-7.97714 - 5.13471i) q^{90} +(12.0530 - 12.0530i) q^{93} +(-7.92672 + 5.75910i) q^{96} +(-4.97879 - 0.788563i) q^{97} +(16.9894 + 8.65651i) q^{98} +10.4029i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{5} + 4 q^{7} - 8 q^{8} + 8 q^{10} - 24 q^{11} - 12 q^{15} + 16 q^{16} - 48 q^{18} - 8 q^{20} + 36 q^{21} - 16 q^{22} + 32 q^{28} + 12 q^{30} + 64 q^{32} + 12 q^{33} + 8 q^{35} - 24 q^{36}+ \cdots + 72 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^5 + 4 * q^7 - 8 * q^8 + 8 * q^10 - 24 * q^11 - 12 * q^15 + 16 * q^16 - 48 * q^18 - 8 * q^20 + 36 * q^21 - 16 * q^22 + 32 * q^28 + 12 * q^30 + 64 * q^32 + 12 * q^33 + 8 * q^35 - 24 * q^36 + 24 * q^42 - 48 * q^45 - 4 * q^50 + 28 * q^55 - 24 * q^56 - 8 * q^58 + 80 * q^59 + 12 * q^63 + 36 * q^66 - 32 * q^70 + 24 * q^72 - 28 * q^73 - 24 * q^75 - 12 * q^77 - 64 * q^80 + 36 * q^81 + 24 * q^83 - 36 * q^87 + 32 * q^88 + 24 * q^93 - 16 * q^97 + 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more